Newsboy model

Till here, we assumed deterministic demands. However in real world scenarios, it is highly likely that demand changes fitting a statistical distribution. Newsboy model is a widely used approach. We can assume the demand D as a random variable. A boy purchases Q newspapers to sell and based on the demand, he has an underage cost c (when demand is more than the number of newspapers, 0 or overage cost Co (when Q is greater than the demand). Then the optimal number of newspapers to purchase is found by ... 

Newsboy model is used in periodic review problems. It ignores set-up cost, (fi. R) policy requires continuous review. Once the inventory level hits R, Q quantity is ordered. In periodic review (, S) policy S-I is ordered if the inventory on hand (/) is less than or equal to s. 

While their in-season demand levels are correlated, both retailers have to order inventory in advance in the start of the season and thus face their own independent single-period demand uncertainty models (newsboy models). Let Xj and X2 refer to the discount factor for early orders, thus the retail prices are (for Retailer 1) andpX2 (for Retailer 2) for early orders. 

The decision described above is commonly termed the newsboy model. The optimal capacity decision can be obtained by identifying two costs the marginal cost of excess capacity Q and the marginal cost of capacity shortage Q. In the example above, the marginal cost of excess capadty is... 

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